On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2010

On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

Javier Turek
  • Fonction : Auteur
Irad Yavneh
  • Fonction : Auteur
Matan Protter
  • Fonction : Auteur

Résumé

Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a pre-specified dictionary. In this work we analyze two Bayesian denoising algorithms -- the Maximum-Aposteriori Probability (MAP) and the Minimum-Mean-Squared-Error (MMSE) estimators, under the assumption that the dictionary is unitary. It is well known that both these estimators lead to a scalar shrinkage on the transformed coefficients, albeit with a different response curve. In this work we start by deriving closed-form expressions for these shrinkage curves and then analyze their performance. Upper bounds on the MAP and the MMSE estimation errors are derived. We tie these to the error obtained by a so-called oracle estimator, where the support is given, establishing a worst-case gain-factor between the MAP/MMSE estimation errors and the oracle's performance. These denoising algorithms are demonstrated on synthetic signals and on true data (images).

Dates et versions

hal-00474157 , version 1 (19-04-2010)

Identifiants

Citer

Javier Turek, Irad Yavneh, Matan Protter, Michael Elad. On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary. 2010. ⟨hal-00474157⟩
79 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More